Ball on a String

Oops! There is another problem that I am stuck on. Here is a recap from my last thread posted this morning...I am finishing an on-line basic physics course. I am taking a self-assessment before the official on-line certification next week. Here is another problem which I am stuck on and require some guidance.

A tennis ball on the end of a string travels in a horizontal circle at a constant speed of 3 m/s. The circle has a radius of 2 m and the centripetal force is 1.5 N. How much work is done on the ball each time it travels around the circle?

I think that all the information given is not required. The obvious formula that has all these variables and was used thoughout the course is W=Fd.
So, a force of 1.2N is exerted throughout the balls orbit. If the radius is 2 m then the circumfrance of the circle is 12.6 [2Pi(r)]. Then W=Fd...W=(1.5N)(12.6m)...W=19. I do not believe this is correct because the answer should be around 12 joules. What did I do wrong? Did I mix up formulas and units? Some guidance please.

Staff: Mentor

You need to understand the formula for the work done by a force: W = F*d.

The "d" stands for the displacement in the direction of the force. In this case, ask yourself: What's the direction of the force? What's the direction of the displacement? What's the angle between them?

If the displacement and force are in the same direction, then the work is simply W = Fd.

If the displacement and force are at an angle (theta) with respect to each other, then the work is W = Fd cos(theta).

I was reviewing my notes and looking in the text, and cos(theta) is not in there at all and I do not understand it. How would I go about finishing this problem to get the correct answer (which i know is 12 Joules)?

the answer is not twelve jewels, at least not so far as i can determine from the problem posted.

the cos theta is for breaking down a vector into a serperate component.

work is only valid when there is displacement parallel to the force exerted. what direction is the force exerted in your system? what is the direction of displacement at one instant. what is the angle between the two?

hopefully this helps, maybe you should draw a diagram viewed from above. that's how i imagined the problem

First, thanks to everyone for responding to my question from an on-line basic physics tutorial. In my problem when I first answered it I got W=19. From what everyone is saying this would be true if my problem had an object moving 12.6 m wiht a force of 1.5 N in a straight line (same direction). Now, in my system a ball is attached to a string 2 m in length, is traveling in a circle with a centripetal force of 1.5 N. I can visualize that there is displacement and a direction to that displacement. I do not know the angle. Is there a way to determine that from my posted question? Also, in the module on this topic there is no mention of the theta angle or a formula that asked for cosine of the angle. The answer of W=12 is given in the tutorial but no work is shown. Any other ideas? What answer do you get for this problem? Why did the problem state the velocity of the ball? Is that fact required to answer this question? Thanks again for all of your help.

You could use W=Fd if you take F the force in the direction of the displacement d. You say there is a centripetal force and a displacement in the shape of a circle. What is the force in the direction of this displacement?

Try not to find 12 Joules but just draw the directions of the force and the displacements. It is a really simple outcome...

I am confused. None of the tutorial related any information regarding angles of a rotating body on a string. Even though I do want to understand and get this problem correct (even if my head explodes). I drew some diagrams but still I am uncertain where to begin. I drew a square 4 m on all sides with a spere (r=2 m) inside the box. I picked a point on the path of the ball (where my sphere in the box touches the side of the box) and it seems that the force moving the ball is in a direction to side of the box that it touches. The attached string will exert a force to keep the ball moving equidistance from the circle's center. When the ball reaches the next side of the box that I drew the exerted force appears to be 45 degrees different than the first force. I am at all on the right track? If I am I still do not know how to proceed. Please...more guidance and help!!!

Staff: Mentor

It's much simpler that you think. First off, forget about that 12 J answer; assuming you've described the problem accurately, it's just plain wrong.

Question: If you were told that someone exert a force F on something, and that something moved a distance D, could you tell us how much work was done by the force? Answer: NO! Depending upon the direction the force acted, the work could range anywhere from F*D to zero!

Example: You hold a 10 N weight in your hand (direction of force you exert: up). If you walk around the room with that weight, how much work do you do on it? Answer: You do 0 work, since the force (in the vertical direction) has no component along the displacement (which is in the horizontal direction).

For your problem, the force acts along the string. Does the object move in that direction?

I was thinking about this last night. Tell me if I am off in my thinking. This rotating ball would fly off at a 90 degree angle to the tangent line (is this the line formed from the center of the circle and extending to the ball). This would make the angle that you are asking me about 90 degrees. If this is correct how do I proceed next with my problem? Thanks.

Once the centripetal force stopped acting on the ball, the velocity would not change. As teclo mentioned, the tangent line is the direction of velocity. Consequently, the ball would fly off parallel to the tangent line, not perpendicular to it.

However, it looks more like you confused the tangent line and the radial line. The radial line is the line described by the position of the ball and the center of the circle. The tangent line will be, hence the name, tangent to the circle. You know from geometry how these two lines are related.

Now, knowing that, remember that the centripetal force is always directed at the center of the circle. Keeping in mind that the ball always follows the path described by its velocity, which direction is the path relative to the force? Here's a hint: You've already said it somewhere in your last post.

Knowing that, how much of the force is in the direction of motion and how does this make the problem almost trivial?